Question

In a poll conducted by a survey firm, 82% of respondents said that their jobs were sometimes or always stressful. Eleven workers are chosen at random for the Binomial experiment. What is the probability that more than 9 of them find their jobs stressful

Answer 1

`P(X >9) = P(X=10) +P(X=11)`

And we can find the individual probabilities with the mas function adn we got:

`P(X=10)=(11C10)(0.82)^(10) (1-0.82)^(11-10)=0.272`

`P(X=11)=(11C11)(0.82)^(11) (1-0.82)^(11-11)=0.113`

And replacing we got:

`P(X>9) =0.272 +0.113= 0.385`

Explanation:

Let X the random variable of interest "number of workers who find their jobs stressful", on this case we now that:

`X \sim Binom(n=11, p=0.82)`

The probability mass function for the Binomial distribution is given as:

`P(X)=(nCx)(p)^x (1-p)^(n-x)`

Where (nCx) means combinatory and it's given by this formula:

`nCx=(n!)/((n-x)! x!)`

We want to find the following probability:

`P(X >9) = P(X=10) +P(X=11)`

And we can find the individual probabilities with the mas function adn we got:

`P(X=10)=(11C10)(0.82)^(10) (1-0.82)^(11-10)=0.272`

`P(X=11)=(11C11)(0.82)^(11) (1-0.82)^(11-11)=0.113`

And replacing we got:

`P(X>9) =0.272 +0.113= 0.385`